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In the 2009-2010 season, I found 443 instances where a team held the ball down three points during their last possession of a period (either the end of the 2nd half or an overtime period). In 391 of those cases, the team leading did not foul. In 52 cases, the team chose to foul. [...]
Of the 52 teams that committed a foul, six lost the game for a winning percentage of 88.46%. Of the 391 teams that did not foul, 33 lost the game for a winning percentage of 91.56%. Both a two sample t-test of proportion and a Chi-squared test fail to reject the null hypothesis that there is a difference in winning percentage between the two strategies. In this sample, teams that did not foul won slightly more often. For the less statistically inclined, this means that there is no significant difference between the two strategies.